Abstract

The uncertainty principle applied to electromagnetic fields implies that the field phase and photon number cannot simultaneously have arbitrarily narrow distributions. Here we describe an experiment which determines, for the first time, the variances of phase and photon number for a field containing small numbers of photons. The measurements allow a test of the uncertainty relation for the phase and photon number of a mode of the electromagnetic field when the field mode is in a very weak coherent state. The phase of the field is described by the Pegg-Barnett phase operator formalism. [1] The measurements are accomplished by experimentally determining the quantum state of the field by using optical homodyne tomography. [2] This method of state characterization requires that an ensemble of many measurements be performed. [3] In this case, the relevant interpretation of the uncertainty relation is that the state of the field does not have well defined phase and photon number.

© 1993 Optical Society of America